A353753 - OEIS

%I #10 May 08 2022 15:39:31

%S 0,0,0,0,0,0,0,0,0,2,0,0,0,0,4,0,0,0,0,0,8,4,0,0,0,0,0,0,0,16,0,0,8,6,

%T 8,0,0,0,12,8,0,16,0,0,0,8,0,0,0,0,12,6,0,0,16,0,16,8,0,24,0,0,0,0,12,

%U 32,0,0,16,32,0,0,0,0,0,0,16,24,0,0,0,12,0,48,24,0,16,16,0,24,24,0,32,16,16,0,0,36

%N a(n) = phi(sigma(n)) - Product_{p^e||n} phi(sigma(p^e)), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

%H Antti Karttunen, <a href="/A353753/b353753.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A062401(n) - A353752(n).

%o (PARI)

%o A062401(n) = eulerphi(sigma(n));

%o A353753(n) = { my(f = factor(n)); A062401(n)-prod(k=1, #f~, A062401(f[k, 1]^f[k, 2])); };

%Y Cf. A000010, A000203, A062401, A353752, A353754, A353755.

%Y Cf. A336547 (positions of 0's), A336548 (positions of terms > 0).

%Y Cf. also A353803.

%K nonn

%O 1,10

%A _Antti Karttunen_, May 08 2022